Normal Force and Friction - Mechanics Step by Step

On flat ground the normal force equals the weight, and friction is a fraction of that normal force resisting any slide.

mechanics A 2 kg block on flat ground gives a clean 20 N normal force, and friction is just a fraction of it.

Example

On flat ground the normal force equals the weight, and friction is a fraction of that normal force resisting any slide. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

On flat ground the normal force equals the weight

A block of mass 2 kilograms rests on flat ground. Its weight is 2 times 10, or 20 newtons down, and the ground pushes back with an equal normal force of 20 newtons up.

N = m\,g = 2\ \text{kg} \,\cdot\, 10\ \text{m}/\text{s}^{2} = \hl{20}\ \text{N}

More mass gives more normal force

Hold gravity fixed. A heavier block has more weight, so flat ground pushes back with a larger normal force.

\begin{array}{c|c|c}m & g & N \\ \hline 1\ \text{kg} & 10\ \text{m}/\text{s}^{2} & 10\ \text{N} \\ 2\ \text{kg} & 10\ \text{m}/\text{s}^{2} & 20\ \text{N} \\ 3\ \text{kg} & 10\ \text{m}/\text{s}^{2} & 30\ \text{N}\end{array}

Stronger gravity gives more normal force

Hold mass fixed. Stronger gravity makes the weight larger, so the normal force must be larger on flat ground.

\begin{array}{c|c|c}m & g & N \\ \hline 2\ \text{kg} & 5\ \text{m}/\text{s}^{2} & 10\ \text{N} \\ 2\ \text{kg} & 10\ \text{m}/\text{s}^{2} & 20\ \text{N} \\ 2\ \text{kg} & 15\ \text{m}/\text{s}^{2} & 30\ \text{N}\end{array}

Friction is proportional to the normal force

Friction acts sideways, resisting sliding, and it is proportional to how hard the surfaces are pressed together, which is the normal force. The friction is some fraction mu of the normal force. That fraction is a property of the two surfaces in contact, found by measurement, not a universal constant like gravity: rougher pairs have a bigger one. We use clean values here. The rule sets how big the friction can get; we split the still case from the sliding case next.

f = \mu\,N

Same surfaces, more normal force, more friction

Hold the surface fraction fixed. Press the surfaces together harder and the friction force grows in the same ratio.

\begin{array}{c|c|c}\mu & N & f \\ \hline \tfrac{3}{10} & 10\ \text{N} & 3\ \text{N} \\ \tfrac{3}{10} & 20\ \text{N} & 6\ \text{N} \\ \tfrac{3}{10} & 30\ \text{N} & 9\ \text{N}\end{array}

Same press, rougher surfaces, more friction

Hold the normal force fixed. A larger measured surface fraction means a larger friction force.

\begin{array}{c|c|c}\mu & N & f \\ \hline \tfrac{1}{10} & 20\ \text{N} & 2\ \text{N} \\ \tfrac{3}{10} & 20\ \text{N} & 6\ \text{N} \\ \tfrac{1}{2} & 20\ \text{N} & 10\ \text{N}\end{array}